Advertisements
Advertisements
Question
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Advertisements
Solution
\[a_n = 2n + 7\]
\[ \therefore a_1 = 2 \times 1 + 7 = 9\]
\[ a_2 = 2 \times 2 + 7 = 11\]
\[ a_3 = 2 \times 3 + 7 = 13\]
\[ a_4 = 2 \times 4 + 7 = 15\]
\[\text { and so on }\]
\[\text { So, common difference }\left( d \right) = 11 - 9 = 2\]
\[\text { Thus, the above sequence is an A . P . with the common difference as} 2\]
\[ a_7 = 2 \times 7 + 7 = 21\]
APPEARS IN
RELATED QUESTIONS
In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nthterm is (2m – 1): (2n – 1)
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
\[\sqrt{2}, 3\sqrt{2}, 5\sqrt{2}, 7\sqrt{2}, . . .\]
The nth term of a sequence is given by an = 2n2 + n + 1. Show that it is not an A.P.
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder 7.
The sum of first 7 terms of an A.P. is 10 and that of next 7 terms is 17. Find the progression.
The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
If a, b, c is in A.P., then show that:
a2 (b + c), b2 (c + a), c2 (a + b) are also in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
If \[a\left( \frac{1}{b} + \frac{1}{c} \right), b\left( \frac{1}{c} + \frac{1}{a} \right), c\left( \frac{1}{a} + \frac{1}{b} \right)\] are in A.P., prove that a, b, c are in A.P.
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
Write the common difference of an A.P. whose nth term is xn + y.
If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term is
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
The first three of four given numbers are in G.P. and their last three are in A.P. with common difference 6. If first and fourth numbers are equal, then the first number is
Show that (x2 + xy + y2), (z2 + xz + x2) and (y2 + yz + z2) are consecutive terms of an A.P., if x, y and z are in A.P.
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n: Sn is equal to ______.
If n AM's are inserted between 1 and 31 and ratio of 7th and (n – 1)th A.M. is 5:9, then n equals ______.
The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.
If b2, a2, c2 are in A.P., then `1/(a + b), 1/(b + c), 1/(c + a)` will be in ______
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.
